While hundreds of millions of Chinese families toasted the new year together, 84-year-old He Daxing huddled on the doorstep of his daughter's home in Chongqing.

On the most important date in the calendar, not one of his six grown children – born before the country's one-child policy was imposed – would take him in.

Filial piety is so embedded here that officials offered to help him sue his offspring when he fell ill after four nights outside: Chinese law requires adults to support their parents. Yet his case shows that traditional ideals are under growing pressure in a fast-changing, increasingly individualistic society.

China may soon have more He Daxings. It faces a soaring number of old people and a shrinking number of young adults, who are also less able – and sometimes less willing – to support their elders.

Life expectancy has soared in China, while fertility has plummeted due to strict birth control policies. In 2009 there were 167 million over-60s, about an eighth of the population. By 2050 there will be 480 million, while the number of young people will have fallen. "It's a timebomb," warned Wang Feng of the Brookings-Tsinghua Centre for Public Policy in Beijing.

China's economic miracle has been fuelled by its "demographic dividend": an unusually high proportion of working age citizens. That population bulge is becoming a problem as it ages. In 2000 there were six workers for every over-60. By 2030, there will be barely two.

Other countries are also ageing and have far lower birth rates. But China is the first to face the issue before it has developed – and the shift is two to three times as fast.

"China is unique: she is getting older before she has got rich," said Wang Dewen, of the World Bank's China social protection team.

Tens of millions of workers have migrated to the cities, creating an even worse imbalance in rural areas which already suffer low incomes, poor public services and minimal social security.

Most old people there rely on their own labour and their children. China not only needs to support more older people for longer, but to extend support to new parts of society. World Bank researchers point to promising advances, such as the national rural pension scheme and the expansion of health insurance.

China can help deal with increased costs by raising its retirement age; at present, only about a fifth of urban women are still working at 55. Improving education should also raise productivity. Some experts believe such measures will be enough to wipe out the "demographic debt". Others wonder if China will begin to welcome immigrants.

Wang Feng thinks China has been far too timid, storing up trouble for the future. "Leaders have ridden the economic boom and largely collected and spent money and built infrastructure – the hardware: railroads, bridges," he said.

"[In future] they will not have the money to spend, but what is more challenging is the part policymakers have stayed away from: building software – the pensions and healthcare system. That will be critical to social stability and regime legitimacy, but it is much harder to do."

The current five-year plan is the first to address ageing. But Wang said leaders had yet to accept it also meant tackling fertility. Under the "one child policy" – which has several exemptions – the fertility rate has dropped to between 1.5 and 1.8, say experts. That is well below the 2.1 figure required to keep the population stable.

Many experts have urged the government to move to a uniform two-child policy. Instead, it has extended what was meant to be a one-generation measure.

China's 150 million only children face a heavier burden of duties, but economic changes such as migration make them harder to fulfil.

In many ways, China is a good place to age. Older people tend to be active, involved and respected community members. Family bonds remain strong.

"Having undutiful children or being an undutiful child is something really shameful in Chinese culture," said Dr Fengshu Liu of Oslo University, who has researched intergenerational relationships.

Society has moved away from the "top-down, authoritarian" family model, but still expects children to meet their parents' physical and emotional needs and often to support them financially.

Officials have been keen to promote such ideals – some have even pushed for laws ordering children to visit regularly – and not just for economic reasons, Liu argued. They see it as helping to preserve stability and social co-operation.

In a more individualistic society relationships face new challenges. Children and their spouses can find their parents' demands excessive or intrusive.

He Daxing's daughters complained he had favoured his sons. And even when personal relations are good, practicalities may intervene. Children may work far from their parents, like one of He's sons, or simply lack time to help.

"I have one daughter and there's no way she will be able to take care of me. I will be in a care home when I get older," predicted Liu Zhongli.

Her pragmatism is unusual, but then Liu is director of Evergreen, a state-owned old people's home in north Beijing. She says that children still love their parents – her facility is inundated with visitors each weekend – but that the pressures of modern life are often overwhelming. "Even if your parents live with you, every day you leave early and come back from work late – so you still leave them at home alone. That's not support and that's not filial," she said.

Increased life expectancy can also mean children need care themselves, like the 88-year-old son of the home's oldest resident, who has just turned 109.

For many, there is still a stigma in moving into a care home. But 86-year-old Zhang Jiazhen tried living with her daughters in the US and said she is happier in Evergreen. "I'm an independent person … I really don't like China's old-fashioned view that you raise sons and daughters to support you when you're old," she said. "I can mix with a bigger family here."

The facilities are modern and comfortable and the atmosphere companionable. Retirees sing together or battle it out at billiard and mahjong tables.

But even if you can afford Evergreen's fees of up to 5,100 yuan (£510) each month, it has just 600 beds, and a waiting list of 1,300. According to the World Bank, China has only enough care home places for 1.6% of over-60s, while in developed countries the capacity is about 8%.

Many of those homes are grim and there is a desperate shortage of good staff: most are unskilled or have little training.

Evergreen is a testing ground for potential solutions. A team from Beijing Aeronautics and Astronautics University are trialling a bed that turns into a wheelchair, giving residents more independence, and a robot "dog" to keep them company. "The robot can have simple chats with them, play music and opera, or even dance for them through sound controls. It says 'It feels so good!' when they pet it," said researcher Zhang Guanxin.

But while such innovations may smooth the later years of wealthier urban citizens, the poor will need help from China's leaders to meet basic needs. Even then, argues Wang Feng, families will face extra strain.

"People who could have had a second child [were it not for the one child policy] have missed the opportunity and when they grow older it is not clear how the government can come to the rescue. In fact, I think it's clear that the government cannot substitute for families," he said.